Math Help: Algebra

Like, I know how to add radicals. But this number outside the radicant keeps pineappleing me up. Can any one give me a step by step process of these two problems? Would be greatly appreciated.

I know for the first one it is supposed to look like this:

(6√2x-1)² = (12+6√x-4)²

But once I factor it I always pineapple it up somehow

For the first one:

Divide both sides by 6
2 = sqrt(2x-1) - sqrt(x-4)

subtract sqrt(2x-1) from both sides
2 - sqrt(2x-1) = - sqrt(x-4)

change the signs to make it easier
sqrt(2x-1) - 2 = sqrt(x-4)

square both sides
2x - 1 - 4sqrt(2x-1) + 4 = x - 4

rearrange
2x+7-x = 4sqrt(2x-1)

square again
x^2 + 14x + 49 = 32x - 16

rearrange
x^2 - 18x + 65 = 0

quadratic formula GO
x = 5, 13 and the sum is 18

For the first one:

Divide both sides by 6
2 = sqrt(2x-1) - sqrt(x-4)

subtract sqrt(2x-1) from both sides
2 - sqrt(2x-1) = - sqrt(x-4)

change the signs to make it easier
sqrt(2x-1) - 2 = sqrt(x-4)

square both sides
2x - 1 - 4sqrt(2x-1) + 4 = x - 4

rearrange
2x+7-x = 4sqrt(2x-1)

square again
x^2 + 14x + 49 = 32x - 16

rearrange
x^2 - 18x + 65 = 0

quadratic formula GO
x = 5, 13 and the sum is 18

This format hurts my eyes

Thank you though, it makes a lot more sense without that pesky 6 there.


asdlksajhdlksjadflkjasfljdfljsals Still struggling to follow this for whatever reason. *Sigh*

Second one is along the same lines.

divide by 2 gets you
1 = sqrt(x-3) - sqrt(2x-4)

rearrange
1 - sqrt(x-3) = -sqrt(2x-4)

change sign
sqrt(x-3) - 1 = sqrt(2x-4)

square both sides
x - 3 - 2sqrt(x-3) + 1 = 2x - 4

rearrange
x - 2sqrt(x-2) - 2 = 2x - 4

then rearrange again
-x + 2 = 2sqrt(x-2)

square
x^2 - 4x + 4 = 4x - 8

rearrange
x^2 = -12

try to solve it and you're sqrting a negative, then you blow up the world. There is no solution.

I threw Rick's into a formatter and got this.

the second one is easy, they give you a limited number of x's to try. trying 3 choices is probably faster than factoring. first one is a better format to make you think. (yeah, i would actually do that on a test. use what your given.)